Download Exciton polarizability in semiconductor nanocrystals

LETTERS
Exciton polarizability in semiconductor
nanocrystals
FENG WANG1 , JIE SHAN2 , MOHAMMAD A. ISLAM3 , IRVING P. HERMAN3 , MISCHA BONN4 AND
TONY F. HEINZ1 *
1
Departments of Physics and Electrical Engineering, Columbia University, New York, New York 10027, USA
Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106, USA
3
Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA
4
FOM-Institute AMOLF, Kruislaan 407, 1098 SJ, Amsterdam, The Netherlands
* e-mail: [email protected]
2
Published online: 8 October 2006; doi:10.1038/nmat1739
he response of charge to externally applied electric fields
is an important basic property of any material system,
as well as one critical for many applications. Here, we
examine the behaviour and dynamics of charges fully confined
on the nanometre length scale. This is accomplished using CdSe
nanocrystals1–3 of controlled radius (1–2.5 nm) as prototype
quantum systems. Individual electron–hole pairs are created at
room temperature within these structures by photoexcitation
and are probed by terahertz (THz) electromagnetic pulses4 .
The electronic response is found to be instantaneous even
for THz frequencies, in contrast to the behaviour reported in
related measurements for larger nanocrystals5 and nanocrystal
assemblies6,7 . The measured polarizability of an electron–hole
pair (exciton) amounts to ∼104 Å3 and scales approximately as
the fourth power of the nanocrystal radius. This size dependence
and the instantaneous response reflect the presence of wellseparated electronic energy levels induced in the system by strong
quantum-confinement effects.
Isolated CdSe nanoparticles, also known as quantum dots
(QDs), were prepared in our laboratory following established wetchemistry procedures2,8 . The particle radius varied from 1.4 to
2.4 nm, with a standard deviation <5%. Because of the strong
quantum confinement in these small QDs, the excited electron and
hole are largely uncorrelated and can be described in a singleparticle picture9 . This system thus provides an attractive model
for the study of the size dependence of the polarizability and
response time of quantum-confined charge carriers. In addition to
the fundamental interest inherent in these questions, an accurate
determination of the behaviour of the quantum-confined electron–
hole pairs provides important information about the excited states
of the CdSe QDs, a topic of significant technological interest for the
potential applications of QDs in lasers10 , light-emitting diodes11 ,
photodetectors and other photovoltaic devices12 .
The polarizability of quantum-confined excitons has previously
been examined using Stark shift measurements13–15 . It is desirable
to have a direct experimental determination of the polarizability—
T
and its dependence on frequency and confinement size. Such
measurements are, however, complicated by the fact that excitons
must be produced by photoexcitation and then exist only for a
duration of nanoseconds16 . This situation suggests the use of a laserbased probe, an approach that can readily achieve the required
temporal resolution and also has the advantage of being noninvasive in nature. In addition, such a probe must interrogate the
system at sufficiently low photon energies to avoid complications
from direct electron or hole transitions, which have energies
of hundreds and tens of meV, respectively, for nanometre-sized
QDs9 . Terahertz (THz) time-domain spectroscopy meets these
requirements: it allows the material response to an electric field
oscillating at frequencies in the THz range (1 THz ≈ 4 meV) to
be recorded with picosecond time resolution17 . The capabilities of
this technique for probing charge-carrier dynamics in photoexcited
systems have been exploited in several recent studies. Among these
are optical-pump/THz-probe measurements of charge transport
and carrier dynamics in bulk solids18–24 and quantum-well
structures25–27 . The method has also been applied, as mentioned
above, to QDs extending to larger radii5 and to QD assemblies6,7 ,
as well as to carrier-cooling dynamics in QDs28 .
The experimental setup for the optical-pump/THz-probe
apparatus has been described previously29 . Excitons in the
semiconductor QDs were created by absorption of the frequencydoubled laser radiation with a photon energy of 3.1 eV. This energy
lies well above the band edge of the QDs, which was located between
2.2 and 2.7 eV, depending on the QD radius. Care was taken to
ensure that the induced material response remained in the linear
regime as a function of pump fluence, with most photoexcited QDs
containing only a single exciton. For this purpose and to avoid other
nonlinear effects such as exciton photoionization, a pump fluence
well below 1 J m−2 was used. All measurements were carried out
with the sample held at room temperature.
To study the response of the CdSe QDs, we first measured the
electric-field waveform E(t ) of the THz probe pulse transmitted
through the unexcited sample. Subsequently, the pump-induced
nature materials VOL 5 NOVEMBER 2006 www.nature.com/naturematerials
©2006 Nature Publishing Group
861
LETTERS
Experiment
3.0
Δ ETHz (×200)
Model
Model
2.5
0
–200
ΔE THz
ETHz ( V cm–1)
200
ETHz
Δ χs' and Δ χs" (10–5 mm)
400
–400
Δ χ 's
2.0
1.5
1.0
0.5
–600
0
30
60
90
Pump–probe delay (ps)
Δ χ ''s
0
0.6
1
2
3
4
0.7
0.8
0.9
Frequency (THz)
1.0
1.1
Time (ps)
Figure 1 THz electric-field waveform transmitted through an unexcited
suspension of CdSe QDs and the photoinduced change in this waveform. The
dashed black line is the result of a calculation assuming a frequency-independent
change in only the real part of the susceptibility. The inset depicts the decay of the
pump-induced change in the transmission of the THz radiation. The photoinduced
THz response was measured at 60 ps after photoexcitation.
change in the THz waveform E(t ) was recorded by chopping the
excitation pulse and monitoring the differential THz signal (that is,
with and without excitation). E(t ) was measured at a delay of
60 ps after the optical excitation. As shown in refs 16,30, exciton
cooling in CdSe QDs occurs in ∼1 ps. Thus, our measurement
scheme ensures that we probe the ground-state exciton, despite
initial optical pumping to higher-lying states. A modest reduction
in the THz signal was observed with increasing pump/probe delays
(inset of Fig. 1), which we attribute to carrier trapping at the QD
interface in a subset of the QDs31 . In our experiment, with a
weak photoinduced change in a relatively thick sample, the effect
of the pump beam can be expressed as a change in the complex
sheet susceptibility of the sample, χs , defined as the change in
the dipole moment per unit area divided by the THz electricfield strength. Expressing the relevant quantities in the frequency
domain29 , we have
E(ω)
2πω χs (ω)
(1)
,
=i
√
E(ω)
c
ε
where c is the speed of light in vacuum, ω is the angular frequency
of the THz radiation and ε is the dielectric function of the unexcited
QD suspension.
In Fig. 1 we show experimental results for the transmitted
THz field E(t ) and the photoinduced modulation E(t ) for
CdSe QDs of 2.0 nm radius. Figure 2 shows the corresponding
frequency-dependent changes in the sheet susceptibility χs (ω) =
χs (ω) + iχs (ω), as calculated from the experimental data
and equation (1). The imaginary part of the susceptibility is seen
to remain essentially unchanged, whereas the change in the real
part is appreciable, but largely frequency-independent over the
investigated frequency range. Indeed, the experimental waveform
for the response, E(t ), can be reproduced numerically by
propagating the measured E(t ) through a sample with a frequencyindependent real susceptibility χs (ω) = χs (dashed lines in
Figs 1 and 2). This response is entirely different from that observed
in a test measurement of a photoexcited CdSe thin film (data not
shown). For the latter case, we found a Drude-like THz response
862
Figure 2 Spectral dependence of the change in the real (χ s ) and imaginary
part (χ s ) of the photoinduced sheet susceptibility of the sample. The grey
lines are obtained from the experimental data of Fig. 1. The dashed lines represent a
frequency-independent and purely real induced susceptibility that corresponds to
the dashed waveform in the time-domain data of Fig. 1.
characteristic of free charges and similar to the behaviour in other
doped or photoexcited semiconductors4 .
Classical transport theory—adapted from the bulk material
with an added term accounting for surface scattering—has been
used to model the THz response of nanoparticles with radii up to
12.5 nm (ref. 5). Such a description is not, however, appropriate
for the small QDs under investigation here. In these QDs, strong
confinement effects occur and the carriers occupy discrete energy
levels separated by at least tens of meV (ref. 9). This situation
invalidates the picture of perturbed bulk transport with charge
carriers moving in a continuous band of states. In the strong
confinement regime, the excitations are more like those of a large
atom than those of a small piece of bulk material. We consequently
consider our measurement as probing the polarizability of the
photogenerated exciton confined in QDs. From the experimental
standpoint, the correctness of this view is confirmed by the
observation that the response to a THz electric field (Fig. 2) is given
by a real and spectrally flat susceptibility. These two features both
follow from the existence of well-separated electronic states that are
probed by THz radiation with photon energies (of ∼4 meV) lying
significantly below the electron and hole transitions.
The experimental measurements yield information about the
THz response of the quantum-confined excitons through the
sheet susceptibility of the photoexcited sample. We can relate this
quantity to the exciton polarizability α of an individual excited
QD by
9ε2
χs = ns
α.
(2)
(εNP + 2ε)2
Here ε = 1.81 is the measured dielectric constant of the suspension,
εNP ≈ 10 is the dielectric constant of the unexcited CdSe (ref. 32)
and ns is the sheet excitation density. The last quantity is
given by the number of incident photons per unit area for
our optically dense sample, which is assumed to have unity
quantum efficiency for exciton generation8 . The relation given
in equation (2) follows from the effective-medium theory33 in
the (experimentally relevant) dilute limit, but without any selfscreening of the exciton.
nature materials VOL 5 NOVEMBER 2006 www.nature.com/naturematerials
©2006 Nature Publishing Group
LETTERS
Experiment
3
Model
α (×104 Å3)
R 4 scaling
2
1
0
1.0
1.5
2.0
Nanoparticle radius R (nm)
2.5
Figure 3 Polarizability of quantum-confined excitons in photoexcited CdSe QDs
as a function of the QD radius R. Experimental data (symbols) and theoretical
predictions based on the multiband effective-mass model described in the text
(dotted line). For comparison, the solid line shows a simple R 4 scaling. The error
bars reflect the reproducibility of the measurements; in addition, there is an overall
uncertainty of a factor of 2 in the vertical scale associated with the experimental
determination of the QD excitation density.
The exciton polarizability α derived in this manner is shown
in Fig. 3 as a function of the size of the QD. The numerical values
of the polarizability are of the order of 10,000 Å3 , three orders
of magnitude larger than typical molecular polarizabilities and
about 10 times larger than that of conjugated oligomer chains of
similar length34 . These results are qualitatively consistent with those
of d.c. Stark effect measurements, which also indicate very large
polarizabilities13–15 . The error bars for α in Fig. 3 correspond to the
reproducibility of the measurement. Because of inhomogeneities in
the spatial profile of the pump beam and possible residual effects
of multiple electron–hole pair excitation in the QDs, the overall
vertical scale is subject to an estimated error up to a factor of 2.
The measured dependence of the polarizability on the QD
radius R can be described reasonably well by the scaling relation
α ∼ R4 (solid line in Fig. 3). This behaviour can be understood from
the usual expression for the linear polarizability: α ∼ |er|2 /E ,
where er is the transition dipole moment and E is a typical
energy-level spacing of the charge carrier. For a carrier confined
within a region of characteristic size R, the dipole moment is of
the order of eR and the energy-level spacing is ∼h2 /mR2 , where m
is the mass of the charge carrier and h is Planck’s constant. Thus,
α ∼ R4 /aB is obtained, where aB denotes the Bohr radius.
To describe the exciton polarizablity more quantitatively,
including both its magnitude and variation with R, we use a more
realistic model of the electronic structure of the QDs within a
multiband effective-mass treatment9 . In the regime of interest with
R < aB (∼5 nm for CdSe), it has been shown that both the energy
levels and wavefunctions for the electron and hole comprising an
exciton are largely uncorrelated9 . Consequently, we can analyse the
excitations within a single-particle picture9 and treat the exciton
polarizability as the sum of contributions from the electron and the
hole, with correction from the interactions treated perturbatively.
In this picture, we obtain the relevant energies and transition
strengths for the electron and hole separately and evaluate
their contributions to the polarizablity (see the Supplementary
Information). The calculations reveal that the hole contribution to
the polarizability dominates over that from the electron, owing to
a larger hole effective mass and the concomitant smaller energylevel spacing. Figure 3 (dotted line) shows the resulting predictions
for the polarizability as a function of QD radius R. The analysis
yields a size dependence of α ∼ R3.6 for the polarizability over the
relevant range of QD radii. The modest deviation from the simple
R4 scaling arises from the non-parabolicity of the electronic bands
and from the electron–hole interaction. The latter effect would
cause α to level off as the size of the QD increases and bulk excitonic
effects emerge. The agreement with the experimentally derived
polarizabilities is surprisingly good considering the experimental
uncertainties and the simplifications inherent in the model.
In the strongly confined QDs studied here, the exciton
response is ‘atom’-like, characterized by a large polarizability
with an instantaneous response up to THz frequencies. A
systematic investigation of QDs of increasing radius will permit
the understanding of possible pathways of the cross-over from
this strongly confined ‘atomic’ response to different types of bulk
behaviour involving excitons or free carriers.
METHODS
SAMPLE PREPARATION
QDs, capped by TOPO (trioctylphosphine oxide, Aldrich), TOP
(trioctylphosphine, Aldrich), and ∼1.5 monolayer of ZnS were synthesized in
our laboratory by wet chemistry2,8 . The radii of the QDs and their size
distribution in any given sample were deduced from the position and width of
the first peak of the absorption spectra following ref. 3. The QDs were probed
in a 1 cm cell containing a dilute suspension of the particles (concentration
<1016 cm−3 ) in 2,2,4,4,6,6,8-heptamethylnonane (Aldrich).
EXPERIMENTAL SETUP
The femtosecond laser source consisted of an amplified, mode-locked
Ti:sapphire system, providing pulses of approximately 200 fs duration at
810 nm with an energy of 1 mJ per pulse and a repetition rate of 1 kHz. The
THz system35 used optical rectification of the femtosecond laser pulses in a
ZnTe crystal for the generation of the THz probe field. The detection of the
THz waveform was accomplished by electro-optic sampling with a
time-synchronized femtosecond laser pulse in a second ZnTe crystal.
Received 9 April 2006; accepted 21 August 2006; published 8 October 2006.
References
1. Woggon, U. Optical Properties of Semiconductor Quantum Dots (Springer, Berlin, 1997).
2. Murray, C. B., Norris, D. J. & Bawendi, M. G. Synthesis and characterization of nearly monodisperse
CdE (E = S, Se, Te) semiconductor nanocrystallites. J. Am. Chem. Soc. 115, 8706–8715 (1993).
3. Norris, D. J. & Bawendi, M. G. Measurement and assignment of the size-dependent optical spectrum
in CdSe quantum dots. Phys. Rev. B 53, 16338–16346 (1996).
4. Schmuttenmaer, C. A. Exploring dynamics in the far-infrared with terahertz spectroscopy. Chem.
Rev. 104, 1759–1779 (2004).
5. Beard, M. C., Turner, G. M. & Schmuttenmaer, C. A. Size-dependent photoconductivity in CdSe
nanoparticles as measured by time-resolved terahertz spectroscopy. Nano Lett. 2, 983–987 (2002).
6. Beard, M. C. et al. Electronic coupling in InP nanoparticle arrays. Nano Lett. 3, 1695–1699 (2003).
7. Cooke, D. G. et al. Anisotropic photoconductivity of InGaAs quantum dot chains measured by
terahertz pulse spectroscopy. Appl. Phys. Lett. 85, 3839–3841 (2004).
8. Hines, M. A. & Guyot-Sionnest, P. Synthesis and characterization of strongly luminescing
ZnS-capped CdSe nanocrystals. J. Phys. Chem. 100, 468–471 (1996).
9. Efros, A. L. & Rosen, M. The electronic structure of semiconductor nanocrystals. Annu. Rev. Mater.
Sci. 30, 475–521 (2000).
10. Klimov, V. I. et al. Optical gain and stimulated emission in nanocrystal quantum dots. Science 290,
314–317 (2000).
11. Colvin, V. L., Schlamp, M. C. & Alivisatos, A. P. Light-emitting-diodes made from cadmium selenide
nanocrystals and a semiconducting polymer. Nature 370, 354–357 (1994).
12. Ginger, D. S. & Greenham, N. C. Charge injection and transport in films of CdSe nanocrystals.
J. Appl. Phys. 87, 1361–1368 (2000).
13. Empedocles, S. A. & Bawendi, M. G. Quantum-confined Stark effect in single CdSe nanocrystallite
quantum dots. Science 278, 2114–2117 (1997).
14. Sacra, A., Norris, D. J., Murray, C. B. & Bawendi, M. G. Stark spectroscopy of CdSe
nanocrystallites—the significance of transition linewidths. J. Chem. Phys. 103, 5236–5245 (1995).
15. Seufert, J. et al. Stark effect and polarizability in a single CdSe/ZnSe quantum dot. Appl. Phys. Lett.
79, 1033–1035 (2001).
16. Klimov, V. I. Optical nonlinearities and ultrafast carrier dynamics in semiconductor nanocrystals.
J. Phys. Chem. B 104, 6112–6123 (2000).
nature materials VOL 5 NOVEMBER 2006 www.nature.com/naturematerials
©2006 Nature Publishing Group
863
LETTERS
17. Beard, M. C., Turner, G. M. & Schmuttenmaer, C. A. Terahertz spectroscopy. J. Phys. Chem. B 106,
7146–7159 (2002).
18. Groeneveld, R. H. M. & Grischkowsky, D. Picosecond time-resolved far-infrared experiments on
carriers and excitons in GaAs-AlGaAs multiple-quantum wells. J. Opt. Soc. Am. B 11,
2502–2507 (1994).
19. Hegmann, F. A., Tykwinski, R. R., Lui, K. P. H., Bullock, J. E. & Anthony, J. E. Picosecond transient
photoconductivity in functionalized pentacene molecular crystals probed by terahertz pulse
spectroscopy. Phys. Rev. Lett. 89, 227403 (2002).
20. Thorsmolle, V. K. et al. Ultrafast conductivity dynamics in pentacene probed using terahertz
spectroscopy. Appl. Phys. Lett. 84, 891–893 (2004).
21. Huber, R. et al. How many-particle interactions develop after ultrafast excitation of an electron–hole
plasma. Nature 414, 286–289 (2001).
22. Shan, J., Wang, F., Knoesel, E., Bonn, M. & Heinz, T. F. Measurement of the frequency-dependent
conductivity in sapphire. Phys. Rev. Lett. 90, 247401 (2003).
23. Averitt, R. D. et al. Ultrafast conductivity dynamics in colossal magnetoresistance manganites. Phys.
Rev. Lett. 87, 17401 (2001).
24. Beard, M. C., Turner, G. M. & Schmuttenmaer, C. A. Transient photoconductivity in GaAs as
measured by time-resolved terahertz spectroscopy. Phys. Rev. B 62, 15764–15777 (2000).
25. Turchinovich, D. et al. Ultrafast polarization dynamics in biased quantum wells under strong
femtosecond optical excitation. Phys. Rev. B 68, 241307 (2003).
26. Muller, T., Parz, W., Strasser, G. & Unterrainer, K. Pulse-induced quantum interference of
intersubband transitions in coupled quantum wells. Appl. Phys. Lett. 84, 64–66 (2004).
27. Kaindl, R. A., Carnahan, M. A., Hagele, D., Lovenich, R. & Chemla, D. S. Ultrafast terahertz probes of
transient conducting and insulating phases in an electron–hole gas. Nature 423, 734–738 (2003).
28. Hendry, E. et al. Direct observation of electron-to-hole energy transfer in CdSe quantum dots. Phys.
Rev. Lett. 96, 057408 (2006).
29. Knoesel, E., Bonn, M., Shan, J. & Heinz, T. F. Charge transport and carrier dynamics in liquids
probed by THz time-domain spectroscopy. Phys. Rev. Lett. 86, 340–343 (2001).
864
30. Underwood, D. F., Kippeny, T. & Rosenthal, S. J. Ultrafast carrier dynamics in CdSe nanocrystals
determined by femtosecond fluorescence upconversion spectroscopy. J. Phys. Chem. B 105,
436–443 (2001).
31. Guyot-Sionnest, P., Shim, M., Matranga, C. & Hines, M. Intraband relaxation in CdSe quantum dots.
Phys. Rev. B 60, R2181–R2184 (1999).
32. Lide, D. R. Handbook of Chemistry and Physics (CRC Press, New York, 1999).
33. Choy, T. C. Effective Medium Theory—Principles and Applications (Oxford Science Publications,
Oxford, 1999).
34. Gelinck, G. H. et al. Measuring the size of excitons on isolated phenylene-vinylene chains: From
dimers to polymers. Phys. Rev. B 62, 1489–1491 (2000).
35. Nahata, A., Weling, A. S. & Heinz, T. F. A wideband coherent terahertz spectroscopy system using
optical rectification and electro-optic sampling. Appl. Phys. Lett. 69, 2321–2323 (1996).
Acknowledgements
Research at Columbia University was supported primarily by the MRSEC Program of the National
Science Foundation under award number DMR-0213574 and by the New York State Office of Science,
Technology and Academic Research (NYSTAR), with additional support from US Department of
Energy, Office of Basic Energy Sciences, through the Catalysis Science Program. Work at Case Western
Reserve University was supported by NSF grant DMR-0349201.
Correspondence and requests for materials should be addressed to T.F.H.
Supplementary Information accompanies this paper on www.nature.com/naturematerials.
Competing financial interests
The authors declare that they have no competing financial interests.
Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/
nature materials VOL 5 NOVEMBER 2006 www.nature.com/naturematerials
©2006 Nature Publishing Group
Supplemental Material
In the following, we present the details of the calculation of the exciton
polarizability as a function of the quantum dot (QD) radius R (using a multiband
effective-mass model. The results of this analysis are shown as the dotted line in Fig. 3.
The low-frequency polarizability of an exciton is determined by the off-resonant
transitions of the electron and hole comprising the photogenerated exciton. In the regime
of interest with QD radii R < aB (~5 nm for CdSe), it has been shown that both the energy
levels and wavefunctions for the electron and hole comprising the exciton are largely
uncorrelated1. Consequently, we can analyze the excitations within a single-particle
picture1 and treat the exciton polarizability as the sum of independent contributions from
the electron and the hole. To calculate the relevant energies and transition strengths for
the hole, we take the Hamiltonian as
v
v v
v v
H hole = H L − K + VQD (rh ) + Ve − h (re , rh ) + Vimage (re , rh ) .
An analogous Hamiltonian can be written for the electron. Here H L − K is the six-band
Luttinger-Kohn Hamiltonian1 , VQD is the confinement potential (taken to be that of an
infinite spherical square well), Ve-h describes the Coulomb interaction energy between the
electron and the hole, and Vimage is the interaction energy from the image charges
associated with the difference in dielectric screening of the QD and the surrounding
v
v
medium. rh and re denote the hole and electron coordinates, respectively. In the strongly
quantum confined regime investigated here, the energies and wavefunctions are
v
determined primarily by the confinement potential embodied in H L − K + VQD (rh ) ;
v v
v v
corrections arising from interactions [ Ve − h (re , rh ) and Vimage (re , rh ) ] are relatively weak and
are calculated within the first-order perturbation theory2.
© 2006 Nature Publishing Group
Within the six-band model, the hole ground state is 1S3/2, and the first P state is
split, in order of increasing energy, into the 1P3/2, 1P5/2, and 1P1/2 levels (using the
nomenclature of Ref.1). The next low-lying hole states are the 2S3/2, 2P3/2, 1S1/2, 2S1/2 …
levels. We have evaluated the transition energies and the transition dipole moments for
all allowed transitions from the lowest 1S3/2 hole state following the method of Ref.1. The
contribution to the ground-state polarizability from the ith transition is given by
2 µi
, where µi is the transition dipole moment and ∆Ei is the transition energy.
αi =
3 ∆Ei
2
The electron polarizability is calculated similarly. We find the hole polarizability to be
much larger than that of the electron. The greater hole contribution is a consequence of
the larger hole effective mass and the corresponding reduction in the level spacing of the
quantum-confined states. For example, for a 2-nm radius QD, the lowest hole transition
has an energy of ~ 50 meV, while the energy of the electron transition is ~ 400 meV. The
exciton polarizability is dominated by the 1S3/2Æ1P3/2 and 1S3/2Æ1P5/2 hole transitions,
which account for > 80% of the total polarizability.
Figure 3 of the manuscript displays the resulting predictions for the polarizability
as a function of QD radius R. The agreement with the trend of the experimental size
dependence is very good. The theory also reproduces the values of the experimentally
derived polarizabilities well.
In view of the possible systematic errors incurred in
analysis of the experimental results (see the main text) and the simplification in this
analysis, agreement at this level may be somewhat fortuitous.
© 2006 Nature Publishing Group
1.
2.
Efros, A. L. & Rosen, M. The electronic structure of semiconductor nanocrystals.
Annu. Rev. Mater. Sci. 30, 475-521 (2000).
Brus, L. E. Electron-electron and electron-hole interactions in small
semiconductor crystallites - the size dependence of the lowest excited electronic
state. J. Chem. Phys. 80, 4403-4409 (1984).
© 2006 Nature Publishing Group
NEWS & VIEWS
QUANTUM DOTS
Artificial atoms for quantum optics
RUDOLF BRATSCHITSCH AND
ALFRED LEITENSTORFER
are in the Department of Physics and the Center for Applied
Photonics at the University of Konstanz, PO Box M695,
D-78457 Konstanz, Germany.
e-mail: [email protected];
[email protected]
hen the size of a semiconductor crystal
reaches the nanometre scale, the electronic
carriers (negative electrons and positive
holes) feel a strong confining potential, and their
energy spectra become discrete. For each of the energy
levels, the electronic state is described by an atomlike wavefunction, that is, a probability distribution
in space very similar to that of electrons bound to a
nucleus. For this reason, semiconductor quantum dots
are often denoted as large ‘artificial atoms’ — large,
because the energy quantization occurs for crystals
containing as many as 104 atoms. Between electron
and hole states, interband transitions accompanied
by optical absorption or emission may occur, giving
rise, like in atoms, to a discrete series of optical lines.
In addition, the absorption and emission wavelengths
can be tuned by simply varying the nanocrystal size,
which changes the degree of carrier confinement:
with decreasing crystal diameter and hence narrower
confinement potential the electron and hole levels
move further and further apart in energy. This
combination of atomic-like optical emission and
tuneability make quantum dots very interesting as a
model system for studying the interaction between
light and charge carriers in matter, in a much more
flexible and controllable way than for atoms.
On page 861 of this issue, Wang et al. add another
crucial piece of information about the behaviour of
optically excited electron–hole pairs, or excitons1,
confined in quantum dots and subject to external
electric fields. They investigated colloidal CdSe
nanocrystals, which are quantum dots chemically
synthesized in liquid solution. Although selfassembled quantum dots currently have superior
quality due to the growth process in ultrahigh vacuum,
they suffer from a lack of flexibility concerning shape
and positioning. Colloidal nanocrystals of spherical,
rod, pyramidal, cubic and even tetrapod geometry may
THz probe field
Colloidal quantum dots are efficient nanoscopic light emitters with interesting
applications from optoelectronics to biomedical imaging. Their polarizability
has now been measured directly by probing the electronic response without
electrical contacts.
Time
W
be synthesized easily. Compared with self-assembled
quantum dots, the size and hence the photon emission
wavelength of colloidal nanocrystals can also be tuned
in a wider range.
The experiment of Wang and co-authors consisted
of measuring the electric polarizability of an optically
generated exciton in colloidal quantum dots of
different sizes. The difficulty of such an experiment
lies in the fact that the optically generated exciton
lives for a very short period. Moreover, it is not at
all simple to connect the nanocrystal to electrical
contacts without heavily influencing its properties.
These obstacles were elegantly overcome by using
ultrafast terahertz time-domain spectroscopy,
which provides the unique possibility of directly
probing the electronic response without applying
electrical contacts. Such techniques have already
been successfully used to reveal fundamental
ultrafast processes in bulk semiconductors and their
nanostructures3,4. Recently, the carrier cooling in
colloidal CdSe quantum dots has been measured5 in
this way. In Wang’s experiment, a visible interband
pump pulse first generates a single exciton in the
quantum dot. Subsequently, a single pulse of farinfrared light probes the polarizability by pushing
the positive and negative electronic charges against
opposite sides of the confining potential well (Fig. 1).
The great advantage of the technique comes also
from the fact that because the measurement is so
fast, the experiment can be done before the exciton
recombines. The exciton polarizability is found to
increase approximately with the fourth power of the
dot radius. There are only small deviations from the
atom-like model, due to the fact that the potential
nature materials | VOL 5 | NOVEMBER 2006 | www.nature.com/naturematerials
©2006 Nature Publishing Group
Figure 1 Schematic view of
the terahertz polarizability
of a photoexcited exciton in
a colloidal semiconductor
quantum dot. Left: When no
electric field is present, the
positive-charge distribution of
the heavy hole (depicted in red)
and the negative charge of the
electron (blue) are both centred
in the middle of a spherical
nanocrystal. Middle: When the
non-resonant electric probe
field of a terahertz transient
is switched on, the electrons
and holes are pushed against
the wall of the quantum dot
potential (depicted in green).
The polarizability is a measure
of how far both charge
distributions are separated
from each other in a given
electric field. Owing to its larger
effective mass, the hole charge
experiences less quantization
effects and is moved closer
to the wall than the electron.
Right: In the second half-cycle
of the terahertz probe transient,
the exciton is polarized in the
opposite direction.
855
NEWS & VIEWS
felt by the carriers has a different shape than that
experienced by electrons in atoms. It is interesting
to note that the contribution of the hole to the
polarizability dominates over the electron owing to the
larger effective mass and hence smaller energy spacing
of hole energy levels. The quantitative values for the
exciton polarizabilities in CdSe colloidal quantum
dots are of the order of 10,000 Å3, that is, three orders
of magnitude larger than typical atomic or molecular
polarizabilities. This is in agreement with earlier
measurements based on the shift of the energy levels
with electric field due to the Stark effect6.
This high polarizability, which can be even
higher in elongated CdSe crystals, or nanorods7,
makes quantum dots particularly attractive not only
for efficient photon-emission devices but also for
fundamental quantum-optics experiments. The first
steps in this direction have already been taken. For
example, the strong coupling of an exciton in a single
nanorod to photons in an optical cavity has been
demonstrated8. A colloidal quantum dot can also
be coupled to a metal nanosystem with plasmonic
resonances by moving a metal nano-antenna placed
on the tip of an atomic force microscope (AFM) in
the close vicinity of the dot9 or by nano-assembling
an antenna–nanocrystal structure on a surface with
an AFM (M. Kahl et al. manuscript in preparation).
Owing to the high degree of flexibility in moving
colloidal particles, complex arrangements with
completely new physical effects and properties may
arise in the future. Many of the experiments that may
be envisioned rely on the possibility of manipulating
excitons in quantum dots by external electric fields.
The demonstration by Wang et al. of a high, atomlike, polarizability is therefore a fundamental piece of
information for the development of semiconductorbased quantum optics.
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
856
Scholes, G. D. & Rumbles, G. Nature Mater. 5, 683–696 (2006).
Wang, F. et al. Nature Mater. 5, 861–864 (2006).
Huber, R. et al. Nature 414, 286–289 (2001).
Bratschitsch, R. & Unterrainer, K. in Encyclopedia of Modern Optics
(eds Guenther, R. D., Steel, D. G. & Bayvel, L.) 168–175 (Elsevier,
Oxford, 2004).
Hendry, E. et al. Phys. Rev. Lett. 96, 057408 (2006).
Empedocles, S. A. et al. Science 278, 2114–2117 (1997).
Li, L. & Alivisatos, A. P. Phys. Rev. Lett. 90, 097402 (2003).
Le Thomas, N. et al. Nano Lett. 6, 557–561 (2006).
Farahani, J. N. et al. Phys. Rev. Lett. 95, 017402 (2005).
MATERIAL WITNESS
Dirty physics
My copy of The New Physics, published
in 1989 by Cambridge University Press,
is much thumbed. Now regarded as a
classic, it provides a peerless overview
of key areas of modern physics, written
by leading experts who achieve the rare
combination of depth and clarity.
It is reasonable, then, to regard the revised edition, just
published as The New Physics for the Twenty-First Century,
as an authoritative statement on what’s in and what’s out
in physics. So it is striking to see materials, almost entirely
absent from the 1989 book, prominent on the new agenda.
Most noticeably, Robert Cahn of Cambridge University
has contributed a chapter called “Physics and Materials”,
which covers topics such as dopant distributions in
semiconductors, liquid-crystal displays, photovoltaics and
magnetic storage. In addition, the chapter by Yoseph Imry
of the Weizmann Institute in Israel, “Small-scale Structure
and Nanoscience”, is a snapshot of one of the hottest
areas of materials science.
All very well, but it begs the question of why materials
science was, according to this measure, more or less
absent from twentieth-century physics but central to that
of the twenty-first. One may have thought that the traditional
image of materials science as an empirical engineering
discipline with a theoretical framework based in classical
mechanics looks far from cutting-edge, and would hardly
rival the appeal of quantum field theory or cosmology.
Topics such as inflationary theory and quantum gravity
are still on the menu. But the new book drops topics that
might be deemed the epitome of physicists’ reputed delight
in abstraction: gone are chapters on grand unified theories,
gauge theories, and the conceptual foundations of quantum
theory. Even Stephen Hawking’s chapter on “The Edge of
Spacetime” has been axed (a brave move by the publishers)
in favour of down-to-earth biophysics and medical physics.
So what took physicists so long to acknowledge its
materials aspects? “Straight physicists alternate between
the deep conviction that they could do materials science
much better than trained materials scientists (they are apt
to regard the latter as fictional) and a somewhat standoffish refusal to take an interest,” claims Cahn.
One could say that physicists have sometimes tried to
transcend materials particularities. “There has been the
thought that condensed matter and material physics is
second-rate dirty, applied stuff,” Imry says. Even though
condensed matter is fairly well served in the first edition,
it tended to be rather dematerialized, couched in terms
of critical points, dimensionality and theories of quantum
phase transitions. But it is now clear that universality has
its limits — high-temperature superconductors need
their own theory, graphene is not like a copper monolayer
nor poly(phenylene vinylene) like silicon.
“Nanoscience has both universal aspects, which has
been much of the focus of modern physics, and variety
due to the wealth of real materials,” says Imry. “That’s a
part of the beauty of this field!”
Philip Ball
nature materials | VOL 5 | NOVEMBER 2006 | www.nature.com/naturematerials
©2006 Nature Publishing Group